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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Invariants of pairs in $\mathrm {SL}(4, \mathbb {C})$ and $\mathrm {SU}(3, 1)$
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by Krishnendu Gongopadhyay and Sean Lawton PDF
Proc. Amer. Math. Soc. 145 (2017), 4703-4715 Request permission


We describe a minimal global coordinate system of order 30 on the $\mathrm {SL}(4,\mathbb {C})$-character variety of a rank 2 free group. Using symmetry within this system, we obtain a smaller collection of 22 coordinates subject to 5 further real relations that determine conjugation classes of generic pairs of matrices in $\mathrm {SU}(3,1)$.
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Additional Information
  • Krishnendu Gongopadhyay
  • Affiliation: Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, S.A.S. Nagar, Sector 81, P. O. Manauli, Pin 140306, India
  • MR Author ID: 866190
  • Email:,
  • Sean Lawton
  • Affiliation: Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, Virginia 22030
  • MR Author ID: 802618
  • ORCID: 0000-0002-7186-3255
  • Email:
  • Received by editor(s): March 3, 2016
  • Received by editor(s) in revised form: December 9, 2016
  • Published electronically: June 16, 2017
  • Communicated by: Michael Wolf
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 4703-4715
  • MSC (2010): Primary 14D20, 20H10; Secondary 20C15, 14L30, 20E05, 30F40, 15B57, 51M10
  • DOI:
  • MathSciNet review: 3691988